parcau {lmomco} | R Documentation

## Estimate the Parameters of the Cauchy Distribution

### Description

This function estimates the parameters of the Cauchy distribution from the trimmed L-moments (TL-moments) having trim level 1.

### Usage

    parcau(lmom)

### Arguments

`lmom` | TL-moments from `TLmoms` with `trim=1`.

### Details

Unlike many of the other distributions in this package, the parameter estimation occurs by passing the data into the function and not from passing of an L-moment object (see `lmom.ub`). Contrast this practice with `pargum` for example.) The reason this is so is because the usual L-moments are undefined for the Cauchy distribution, but the trimmed L-moments with a symmetrical trimming parameter are defined. Specifically, the L-moments by trimming the smallest and largest order statistic expections of the Cauchy are defined by Elamir and Seheult (2003). The function `parcau` calls `TLlmoms(x,trim=1)`) internally to compute the trimmed L-moments. The relation between the parameters and the trimmed L-moments is

xi = λ^{(1)}_1 mbox{and}

α = frac{λ^{(1)}_2}{0.698} mbox{.}

### Value

An R `list` is returned.

`type` | The type of distribution: `cau`.
`para` | The parameters of the distribution.
`source` | The source of the parameters: “parcau”.

### Author(s)

W.H. Asquith

### References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, vol. 43, pp. 299–314.

Gilchrist, W.G., 2000, Statistical modeling with quantile functions: Chapman and Hall/CRC, Boca Raton, FL.

### See Also

`TLmoms`, `lmomcau`

### Examples

    X1 <- rcauchy(20)
    parcau(TLmoms(X1,trim=1))

[Package lmomco version 0.92 Index]